8.2 operations with matrices
... For the product of two matrices to be defined, the number of columns of the first matrix must equal the number of rows of the second matrix. A ...
... For the product of two matrices to be defined, the number of columns of the first matrix must equal the number of rows of the second matrix. A ...
Lecture 7: Definition of an Inverse Matrix and Examples
... Lecture 7: Definition of an Inverse Matrix and Examples In the previous lecture we gave examples of pairs of nxn matrices whose products were the identity matrix: the elementary matrices and the diagonal matrices with non-zero diagonal components. In the case of elementary matrices, these correspond ...
... Lecture 7: Definition of an Inverse Matrix and Examples In the previous lecture we gave examples of pairs of nxn matrices whose products were the identity matrix: the elementary matrices and the diagonal matrices with non-zero diagonal components. In the case of elementary matrices, these correspond ...
18.06 Linear Algebra, Problem set 2 solutions
... Thus S + T is closed under addition and scalar multiplication; in other words, it satisfies the two requirements for a vector space. (b) If S and T are distinct lines, then S + T is a plane, whereas S ≤ T is not even closed under addition. The span of S ≤ T is the set of all combinations of vectors i ...
... Thus S + T is closed under addition and scalar multiplication; in other words, it satisfies the two requirements for a vector space. (b) If S and T are distinct lines, then S + T is a plane, whereas S ≤ T is not even closed under addition. The span of S ≤ T is the set of all combinations of vectors i ...